This invention relates to a computational aid for the determination of range, for example of a target ship from a submarine, by a passive sonar technique of observing bearing changes of the target ship as the ranging vessel performs a predetermined maneuver in which its own courses and speeds are known. One such technique is known as Ekelund ranging and involves the recording, usually graphically against time, of the bearings of the target at timed intervals while the ranging or "own" ship is making good a first course and speed having a component crossing the line of sight between the ships, and then changing course of the own ship and again recording the target ship bearings. The slopes of lines faired through the time/bearing plot are indicative of average rate of change of bearing. The angles made by these lines with respect to the time axis of the plot may be utilized, together with the known own ship's speeds across the line of sight, to trigonometrically calculate the range of the target ship.
Heretofore this has been done by actually measuring the slope of each bearing rate line with a bearing rage template, computing algebraically a numerical value of change in bearing rate (.DELTA.B), obtaining a numerical value for change in own ship speed across the line of sight (.DELTA.V), and setting these numerical values into a circular slide rule to obtain the Ekelund range (R.sub.E) in accordance with the formula: EQU R.sub.E =K (.DELTA.V/.DELTA.B),
where K is a scaling factor.
An analysis of detailed data and calculations on a substantial number of Ekelund range determination in a controlled exercise has indicated the following facts.
Approximately 15% of the rangings analyzed had some type of mistake in the slide rule computation of range which caused an error greater than should be expected considering the degree of accuracy which can be obtained from the slide rule in use.
25% (7 of 28) of the rangings examined had bearing rate estimates on at least one leg which differed significantly (greater than 25%) from the computed values of least square fit lines drawn through the bearings. Three of these seven cases were due to mistakes in determining the slopes from the bearing rate template currently used in passive ranging and these produced errors in the final ranges of 34.5%, 48.9%, and 205.5%. The remaining four cases appeared to be due to improper fairing of the line through the bearings and caused errors in the computed ranges between 21% and 38%.
In many range calculations, errors of more than one type were present. A total of 32% of the 28 rangings examined had some type of numerical mistake in either the interpretation of the bearing rate, multiplication of a velocity by a trigonometric function or in the slide rule calculation of range.
The exercise results discussed above indicate a need for improvement in two particular areas. These are reduction in human error incurred in range solutions and improvement in ranging maneuvers. The situation with regard to the second area is complex, because obtaining an accurate range determination is not the only concern of the attacking submarine. He must close his target and at the same time maintain a reasonably low probability of counter-detection. During this process he must perform ranging maneuvers to the extent which the tactical situation permits and the most pressing requirement is perhaps for some way of determining just how good the ranging maneuvers which he has performed are, in terms of probable ranging accuracy.